I don't post much but figured I'd chime in here seeing as I own both the Bose Compact and bought a LD Maui 11 from Frankie V. a few months ago. IMO the Maui 11 sounds a little more balanced with the high,mid and low out of the box. It just seems to have a smoother sound to me. When listening side by side the Bose has a brighter tone which is not necessarily a bad thing. I love the Bose. I just prefer a more mellower sound.
I use a mixer with 2 keyboards, a guitar and 2 vocals and the Maui handles it fine. This is just my opinion and I bet if you were in a noisy place nobody would know the difference between the two. Feel free to ask any questions and I'll try to answer them.